What Force Must Be Applied to the Tip of the Wing to Store Twice the Energy Found in Part (B)?

Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy

Mastering Physics Solutions

Affiliate 8 Potential Energy And Conservation Of Energy Q.1CQ
Is it possible for the kinetic energy of an object to be negative? Is information technology possible for the gravitational potential energy of an object to be negative? Explain.
Solution:

Chapter 8 Potential Free energy And Conservation Of Free energy Q.1P

Solution:

Chapter viii Potential Free energy And Conservation Of Energy Q.2CQ
An avalanche occurs when a mass of snow slides down a steep mountain slope. Discuss the free energy conversions responsible for water vapor rise to class clouds, falling as snow on a mountain, and so sliding downwards a slope as an avalanche.
Solution:
As water vapor rises, at that place is an increase in the gravitational potential energy of the system. Office of this potential free energy is released as snowfall and falls onto the mountain. If an avalanche occurs, the snow on the mountain accelerates downwards the slope, converting more gravitational potential energy into kinetic energy.

Chapter 8 Potential Energy And Conservation Of Free energy Q.2P

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Chapter eight Potential Free energy And Conservation Of Energy Q.3CQ
If the stretch of a leap is doubled, the forcefulness it exerts is too doubled. By what cistron does the spring'south potential energy increment?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.3P

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Chapter 8 Potential Energy And Conservation Of Energy Q.4CQ
When a mass is placed on tiptop of a vertical leap, the spring compresses and the mass moves downward. Analyze this system in terms of its mechanical energy.
Solution:

The initial mechanical energy of the system is the gravitational potential free energy of the mass-Earth system. As the mass moves downwards, the gravitational potential energy of the system decreases.
At the aforementioned fourth dimension, the potential free energy of the spring increases considering information technology is compressed. Initially, the decrease in gravitational potential energy is greater than the increase in the spring's potential energy, which ways that the mass gains kinetic energy. Somewhen, the increase in the bound's energy equals the subtract in the gravitational energy, and the mass comes to rest.

Affiliate 8 Potential Energy And Conservation Of Free energy Q.4P

Solution:

Chapter viii Potential Energy And Conservation Of Free energy Q.5CQ
If a spring is stretched so far that it is permanently deformed, its force is no longer bourgeois. Why?
Solution:

We know that the external force must exist equal to the restoring force, and its direction is opposite to the management of the restoring force. If the external force is greater than the restoring force, and then the spring gets permanently deformed. In this situation, the work that was done to stretch the spring is non fully recovered. Some of the work is converted into the energy of the deformation. For this reason, the bound force is non conservative during deformation.

Affiliate 8 Potential Energy And Conservation Of Energy Q.5P

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Chapter 8 Potential Energy And Conservation Of Energy Q.6CQ
An object is thrown up to a person on a roof. At what point is the object'due south kinetic energy at maximum? At what signal is the potential energy of the system at maximum? At what locations do these energies have their minimum values?
Solution:
When the object is first thrown up, its speed and its kinetic energy are at a maximum. Its potential free energy is cipher at that moment.

(i) The potential energy of the system is at a maximum at the highest point of the object's flight and is at a minimum at the starting point of its journeying (when it has just been released).
(ii) The kinetic energy of the system is at maximum when the object has just been thrown up and is at a minimum when it reaches its highest signal of flight.

Chapter viii Potential Energy And Conservation Of Free energy Q.6P

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.7CQ
It is a law of nature that the total free energy of the universe is conserved. What do politicians mean, then, when they urge "energy conservation"?
Solution:
When the term "energy conservation" is used in everyday language, information technology doesn't refer to the full amount of energy in the universe. Instead it refers to using energy wisely, peculiarly when a particular source of energy like oil or natural gas is finite and non-renewable.

Chapter 8 Potential Energy And Conservation Of Free energy Q.7P
Predict/Explicate Ball 1 is thrown to the footing with an initial downwards speed; ball 2 is dropped to the ground from rest. Assuming the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than, less than, or equal to the alter in gravitational potential energy of ball 2? (b) Choose the best caption from among the following:
I. Ball 1 has the greater total energy, and therefore more energy tin can go into gravitational potential energy.
II. The gravitational potential free energy depends only on the mass of the ball and the drop peak.
3. All of the initial free energy of brawl 2 is gravitational potential energy.
Solution:
(a) The modify in gravitational potential energy of the brawl 1 is equal to the change in gravitational potential free energy of the ball 2.
(b) This is considering the modify in gravitational potential free energy depends only on the mass of the brawl and the height from which the ball is dropped. Therefore choice II is the all-time explanation.

Chapter 8 Potential Free energy And Conservation Of Free energy Q.8CQ

Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.8P
A mass is fastened to the lesser of a vertical jump. This causes the spring to stretch and the mass to motion downward. (a) Does the potential energy of the leap increase, decrease, or stay the aforementioned during this process? Explain. (b) Does the gravitational potential energy of the World-mass system increase, decrease, or stay the same during this process? Explain.
Solution:

Chapter viii Potential Energy And Conservation Of Free energy Q.9CQ

Solution:
We accept a photo which shows an earthmover digging the earth and lifting it and loading it on the truck. In this situation, there are both conservative and non-conservative works involved.
Initially, the engine of the earthmover does positive, non-bourgeois piece of work as it digs out and lifts a load of rocks. At the same time, gravity does negative, conservative work on the rocks every bit the gravitational potential energy of the arrangement increases. As the rock is transported to the truck, the earthmover does positive, non-conservative work. When the rocks are released, gravity does positive, conservative work every bit the gravitational potential energy of the system is converted into kinetic free energy. The kinetic energy of the rocks is converted into sound and heat when they are loaded into the truck.
As the truck is loaded, the spring is compressed. The potential free energy is stored in the form of the bound's potential energy, and the work done by the truck is bourgeois.

Affiliate 8 Potential Free energy And Conservation Of Energy Q.9P
As an Acapulco cliff diver drops to the water from a superlative of 46 thou, his gravitational potential energy decreases by 25,000 J. What is the diver's weight in newtons?
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Chapter 8 Potential Energy And Conservation Of Free energy Q.10CQ
A toy frog consists of a suction loving cup and a spring. When the suction cup is pressed confronting a smooth surface, the frog is held down. When the suction loving cup lets become, the frog leaps into the air. Discuss the behavior of the frog in terms of energy conversions.
Solution:
The toy frog consists of a suction cup and a jump. When the suction loving cup is pressed, the energy of the toy is stored in the form of the jump as potential energy. When the suction cup lets go, and then all its potential energy is converted into kinetic free energy. Every bit a outcome, the frog leaps into the air. The total free energy of the organization is conserved.

Chapter 8 Potential Free energy And Conservation Of Energy Q.10P
Find the gravitational potential energy of an 88-kg person standing atop Mt. Everest at an distance of 8848 yard. Use ocean level as the location for y = 0.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.11CQ
If the force on an object is zero, does that mean the potential free energy of the system is nada? If the potential energy of a organisation is nada, is the forcefulness zero?
Solution:
No
Zero force implies a null rate of change in the potential energy. However, the value of the potential energy tin can be annihilation at all. Similarly, if the potential energy is zero, it does not hateful that the strength is zero. Again, what matters is the rate of change of the potential energy.

Chapter 8 Potential Free energy And Conservation Of Energy Q.11P
Jeopardy! Contestante on the game show Jeopardy! depress spring-loaded buttons to "buzz in" and provide the question corresponding to the revealed answer. The strength abiding on these buttons is about 130 N/thousand. Estimate the amount of energy information technology takes—at a minimum—to buzz in.
Solution:

Chapter viii Potential Energy And Conservation Of Energy Q.12CQ

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Chapter 8 Potential Energy And Conservation Of Energy Q.12

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Chapter viii Potential Energy And Conservation Of Energy Q.13CQ
When a ball is thrown upwardly, it spends the same corporeality of time on the style up as on the mode downwards—every bit long equally air resistance can be ignored. If air resistance is taken into business relationship, is the time on the mode down the same every bit, greater than, or less than the fourth dimension on the mode upward? Explicate.
Solution:
If the air resistance is taken into business relationship, then the total mechanical energy of the system decreases. The distance covered by the brawl is the same on the way downwards every bit it is on the way up, and so the amount of fourth dimension volition be adamant by the boilerplate speed of the ball on the 2 portions of its trip. Note that air resistance does negative, non-conservative work continuously on the ball as it moves. Therefore, its total mechanical energy is less on the way down than information technology is on the style up, which means that its speed at any given pinnacle is less on the way downward. It follows that more time is required for the down portion of the trip.

Chapter 8 Potential Free energy And Conservation Of Energy Q.13P
A vertical spring stores 0.962 J in leap potential energy when a 3.five-kg mass is suspended from it. (a) By what multiplicative factor does the spring potential free energy change if the mass attached to the spring is doubled? (b) Verify your answer to part (a) by calculating the leap potential energy when a 7.0-kg mass is attached to the leap.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.14P
Pushing on the pump of a soap dispenser compresses a minor jump. When the bound is compressed 0.fifty cm, its potential energy is 0.0025 J. (a) What is the force constant of the leap? (b) What pinch is required for the leap potential energy to equal 0.0084 J?
Solution:

Chapter eight Potential Energy And Conservation Of Free energy Q.15P
A forcefulness of 4.1 N is required to stretch a certain spring past 1.4 cm. (a) How far must this bound be stretched for its potential free energy to be 0.020 J? (b) How much stretch is required for the leap potential free energy to be 0.080 J?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.16P
The piece of work required to stretch a certain spring from an elongation of iv.00 cm to an elongation of 5.00 cm is 30.5 J. (a) Is the work required to increase the elongation of the spring from 5.00 an to half dozen.00 cm greater than, less than, or equal to thirty.five J? Explain. (b) Verify your answer to part (a) by calculating the required work.
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Affiliate 8 Potential Energy And Conservation Of Energy Q.17P

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Chapter 8 Potential Energy And Conservation Of Energy Q.18P
Predict/Explain You throw a ball upward and allow information technology fall to the ground. Your friend drops an identical ball straight downwards to the ground from the same top. Is the change in kinetic energy of your brawl greater than, less than, or equal to the change in kinetic energy of your friend's ball? (b) Choose the best caption from amidst the following:
I. Your friend's ball converts all its initial energy into kinetic free energy.
Ii. Your ball is in the air longer, which results in a greater change in kinetic energy.
III. The change in gravitational potential energy is the same for each ball, which means the change in kinetic energy must be the same also.
Solution:
(a) The Change in kinetic energy of your ball is equal to the change in kinetic energy of your friend'due south brawl.
(b) Equally both of you are at the same height, so when the balls come to the ground both balls lose same corporeality of potential energy. Therefore alter in potential energy of the two balls is same. Then from conservation of energy the change in kinetic free energy is also same.
So, choice Three is the best explanation.

Chapter viii Potential Energy And Conservation Of Energy Q.19P
Suppose the state of affairs described in Conceptual Checkpoint viii-two is repeated on the fictional planet Epsilon, where the acceleration due to gravity is less than it is on the Earth. (a) Would the tiptop of a hill on Epsilon that causes a reduction in speed from iv m/s to 0 be greater than, less than, or equal to the summit of the corresponding hill on Earth? Explicate. (b) Consider the colina on Epsilon discussed in part (a). If the initial speed at the bottom of the loma is 5 m/s, volition the final speed at the summit of the colina be greater than, less than, or equal to 3 m/s? Explicate.
Solution:
Solution:
(a) As we are considering on a planet Epsilon where the dispatch due to gravity is less than that on the earth and as the gravitational potential energy is mgh and so larger height would exist needed to proceeds the same level of gravitational potential energy. Thus, a higher hill would be needed.
(b) The initial speed at the bottom of the Epsilon is 5m/due south which are the same on the earth. Since the values of the initial kinetic energy & last potential energies are the same on the Epsilon.
So therefore the concluding speed at the elevation of the colina on Epsilon is the same which is 3m/south

Affiliate 8 Potential Energy And Conservation Of Free energy Q.20P
Predict/Explain When a ball of mass thousand is dropped from. rest from a elevation h, its kinetic energy simply earlier landing is K. Now, suppose a 2nd ball of mass Am is dropped from residue from a summit h/iv. (a) Only before brawl 2 lands, is its kinetic energy 4K, 2K, Thousand, Thousand/2, or Chiliad/4? (b) Choose the best explanation from among the following:
I. The 2 balls have the aforementioned initial free energy.
Two. The more than massive ball will have the greater kinetic energy.
III. The reduced drop tiptop results in a reduced kinetic energy.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.21P
Predict/Explain When a ball of mass m is dropped from rest from a height h, its speed just before landing is v. Now, suppose a second brawl of mass 4m is dropped from rest from a elevation h/4. (a) But earlier ball 2 lands, is its speed 4v, 2v, v, 5/two, or v/4? (b) Choose the best explanation from amidst the following:
I. The factors of 4 cancel; therefore, the landing speed is the aforementioned.
II. The 2 assurance state with the same kinetic energy; therefore, the ball of mass 4m has the speed v/2.
III. Reducing the height by a cistron of 4 reduces the speed by a factor of 4.
Solution:

Affiliate 8 Potential Free energy And Conservation Of Energy Q.22P

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Chapter 8 Potential Free energy And Conservation Of Energy Q.23P

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Chapter 8 Potential Energy And Conservation Of Energy Q.24P
At an entertainment park, a swimmer uses a h2o slide to enter the principal pool. If the swimmer starts at residue, slides without friction, and descends through a vertical top of 2.31 1000, what is her speed at the bottom of the slide?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.25P
In the previous problem, observe the swimmer's speed at the bottom of the slide if she starts with an initial speed of 0.840 grand/south.
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.26P
A player passes a 0.600-kg basket ball downcourt for a fast break. The ball leaves the player's easily with a speed of viii.30 m/s and slows downward to 7.ten m/southward at its highest betoken. (a) Ignoring air resistance, how loftier above the release indicate is the ball when it is at its maximum tiptop? (b) How would doubling the brawl'due south mass affect the result in function (a)? Explain.
Solution:

Affiliate 8 Potential Energy And Conservation Of Free energy Q.27P

Solution:
Here the all the iii balls are at aforementioned tiptop when they reached to the dashed line. And all the assurance started from same height. Therefore the proceeds in potential energy of the three balls is same. Therefore the loss in kinetic energy of each brawl is same. Too all the three balls have same initial speed. So all the iii assurance started with same speed and lost equal amount of kinetic energy. Therefore all the 3 balls take aforementioned speed at the dashes line. And so, selection (C) is correct.

Affiliate 8 Potential Free energy And Conservation Of Free energy Q.28P
In a tennis lucifer, a histrion wins a point by hitting the ball sharply to the ground on the opponent'southward side of the internet. (a) If the ball bounces upwards from the ground with a speed of 16 yard/s, and is caught past a fan in the stands with a speed of 12 yard/s, how high above the court is the fan? Ignore air resistance. (b) Explain why it is not necessary to know the mass of the lawn tennis ball.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.29P

Solution:
Hither the all the three balls are at same meridian when they reached to the dashed line. And all the balls started from same peak. Therefore the gain in potential free energy of the 3 assurance is aforementioned. Therefore the loss in kinetic energy of each ball is aforementioned. Also all the three balls accept same initial speed. So all the three balls started with same speed and lost equal corporeality of kinetic free energy. Therefore all the three balls have aforementioned speed at the dashes line. And so, option (C) is correct.

Chapter eight Potential Energy And Conservation Of Energy Q.30P
A ii.nine-kg block slides with a speed of 1.6 yard/s on a frictionless horizontal surface until information technology encounters a spring. (a) If the block compresses the bound four.eight cm before coming to residuum, what is the strength constant of the spring? (b) What initial speed should the block take to compress the bound by 1.ii cm?
Solution:

Affiliate viii Potential Free energy And Conservation Of Energy Q.31P
A 0.26-kg rock is thrown vertically upwardly from the top of a cliff that is 32 k loftier. When it hits the footing at the base of operations of the cliff, the rock has a speed of 29 thousand/s. Assuming that air resistance tin can be ignored, detect (a) the initial speed of the rock and (b) the greatest height of the rock every bit measured from the base of the cliff.
Solution:

Affiliate 8 Potential Free energy And Conservation Of Free energy Q.32P
A 1.40-kg block slides with a speed of 0.950 m/s on a frictionless horizontal surface until information technology encounters a spring with a strength constant of 734 N/thou. The block comes to rest after compressing the spring four.15 cm. Find the spring potential energy, u, the kinetic energy of the cake, M, and the full mechanical energy of the system, E, for compressions of (a) 0 cm, (b) 1.00 cm, (c) 2.00 cm, (d) 3.00 cm, and (e) four.00 cm.
Solution:

Chapter eight Potential Energy And Conservation Of Energy Q.33P
A v.76-kg stone is dropped and immune to fall freely. Find the initial kinetic energy, the final kinetic energy, and the alter in kinetic free energy for (a) the first two.00 m of fall and (b) the 2nd ii.00 m of fall.
Solution:

If the mass of the bob increases, then the offset office in the above equation decreases hence the speed of bob at point A increases. Therefore, the answer to part (b) increases as the mass increases.

Chapter viii Potential Free energy And Conservation Of Energy Q.34P

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.35P
In the previous problem, (a) what is the bob's kinetic energy at point B? (b) At some point the bob will come to rest momentarily. Without doing an additional calculation, determine the change in the system's gravitational potential energy betwixt point B and the point where the bob comes to rest. (c) Find the maximum angle the string makes with the vertical as the bob swings back and forth. Ignore air resistance.
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.36P

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Chapter eight Potential Energy And Conservation Of Energy Q.37P

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Affiliate viii Potential Energy And Conservation Of Energy Q.38P
You lot coast up a loma on your bicycle with decreasing speed. Your friend pedals up the hill with abiding speed. (a) Ignoring friction, does the mechanical energy of the you-bike-Globe system increase, decrease, or stay the same? Explain. (b) Does the mechanical free energy of the friend-bike-Earth system increment, decrease, or stay the aforementioned? Explain.
Solution:
(A) When a person coasts upwards a hill on his bicycle with decreasing speed, no non-conservative piece of work is done on his bicycle. Therefore, his mechanical free energy is conserved even though his speed decreases.
(B)
To maintain a constant speed, his friend volition have to do positive non-conservative work while going uphill. Thus, his friend's mechanical energy will increase.

Chapter eight Potential Free energy And Conservation Of Free energy Q.39P
Predict/Explain On reentry, the infinite shuttle's protective heat tiles become extremely hot. (a) Is the mechanical energy of the shuttle-World system when the shuttle lands greater than, less than, or the same equally when it is in orbit? (b) Choose the best explanation from amid the following:
I. Dropping out of orbit increases the mechanical energy of the shuttle.
Two. Gravity is a conservative force.
Three. A portion of the mechanical energy has been converted to rut energy.
Solution:
The mechanical energy E of a organisation is the sum of potential free energy U and kinetic energy One thousand.
Not bourgeois forces might decrease the mechanical free energy past converting it to heat energy, or increase it by converting muscular piece of work to kinetic or potential energy.
(a)
The space shuttle'due south protective rut tiles become extremely hot, means that some amount of mechanical free energy is converted to heat free energy due to some non-conservative forces, and total mechanical energy of the system will decrease.
Thus, the mechanical energy of shuttle-World arrangement when the shuttle lands is that of the mechanical energy when the shuttle is in orbit.
(b)
The space shuttle's protective heat tiles get extremely hot, ways that some corporeality of mechanical energy has been converted to heat energy.
Thus, the correct option is .

Affiliate eight Potential Energy And Conservation Of Energy Q.40P
Communicable a moving ridge, a 77-kg surfer starts with a speed of 1.3 m/s, drops through a pinnacle of ane.65 thousand, and ends with a speed of 8.2 g/s. How much nonconservative work was washed on the surfer?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.41P
At a playground, a 19-kg child plays on a slide that drops through a top of ii.three k. The child starts at rest at the tiptop of the slide. On the style down, the slide does a nonconservative work of —361 J on the kid. What is the child'south speed at the bottom of the slide?
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.42P
Starting at rest at the edge of a swimming puddle, a 72.0-kg athlete swims along the surface of the water and reaches a speed of 1.20 grand/s past doing the work Wnc1 = + 161 J. Notice the nonconservative work, Wnc2, done by the water on the athlete.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.43P
A 17,000-kg airplane lands with a speed of 82 m/s on a stationary aircraft carrier deck that is 115 m long. Find the piece of work washed past nonconservative forces in stopping the plane.
Solution:

Chapter viii Potential Energy And Conservation Of Energy Q.44P
The commuter of a 1300-kg auto moving at 17 chiliad/southward brakes quickly to eleven thousand/s when he spots a local garage auction. (a) Discover the change in the car's kinetic energy. (b) Explain where the "missing" kinetic energy has gone.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.45P
Y'all ride your bicycle down a hill, maintaining a constant speed the unabridged time. (a) Equally you ride, does the gravitational potential energy of the y'all-bike-Earth system increase, decrease, or stay the aforementioned? Explain. (b) Does the kinetic energy of you and your bike increase, subtract, or stay the same? Explicate. (c) Does the mechanical energy of the you-bicycle-Earth organization increase, decrease, or stay the same? Explain.
Solution:
Solution:
(a) The gravitational potential energy of the earth-bike-rider system should decrease.
Since the position of the biker could eventually drop to basis level height, the potential energy of the system could get down to zero.
(b) Since the speed is constant throughout the entire time. The kinetic energy of yous & your bike remains the aforementioned
(c) The mechanical free energy of the organisation subtract. Since the total mechanical energy is equal to the sum of potential energy and kinetic energy. Every bit the potential energy decreases & kinetic energy remains the aforementioned. So therefore the mechanical energy of the system decreases.

Chapter viii Potential Energy And Conservation Of Free energy Q.46P
Suppose the system in Example starts with m2 moving downward with a speed of 1.3 m/s. What speed do the masses have just before m2 lands?
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.47P
A 42.0-kg seal at an amusement park slides from rest down a ramp into the pool below. The top of the ramp is one.75 m college than the surface of the h2o, and the ramp is inclined at an bending of 35.0° in a higher place the horizontal. If the seal reaches the water with a speed of 4.xl m/s, what are (a) the work done by kinetic friction and (b) the coefficient of kinetic friction between the seal and the ramp?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.48P
A i.9-kg rock is released from rest at the surface of a pond i.viii one thousand deep. As the rock falls, a constant upward force of 4.6 Due north is exerted on it by water resistance. Calculate the nonconservative work, Wnc, done past water resistance on the rock, the gravitational potential energy of the arrangement, u, the kinetic energy of the rock, 1000, and the total mechanical energy of the organization, E, when the depth of the rock below the water's surface is (a) 0 m, (b) 0.50 m, and (c) one.0 thousand. Permit y = 0 be at the bottom of the pond.
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.49P
A 1250-kg car drives up a hill that is 16.two k loftier. During the bulldoze, two nonconservative forces do work on the car: (i) the forcefulness of friction, and (ii) the force generated by the car'due south engine. The piece of work washed by friction is −iii.eleven × 105 J; the piece of work done by the engine is + vi.44 × 105 J. Notice the change in the car'southward kinetic energy from the bottom of the hill to the top of the loma.
Solution:

Chapter viii Potential Free energy And Conservation Of Energy Q.50P
An 81.0-kg in-line skater does + 3420 J of nonconservative work by pushing against the ground with his skates. In addition, friction does −715 J of nonconservative work on the skater. The skater'southward initial and final speeds are two.50 m/s and 1.22 k/s, respectively. (a) Has the skater gone uphill, downhill, or remained at the same level? Explain. (b) Summate the change in height of the skater.
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.51P
In Case, suppose the 2 masses outset from rest and are moving with a speed of ii.05 yard/s just earlier m2 hits the floor. (a) If the coefficient of kinetic friction is µk = 0.350, what is the distance of travel, d, for the masses? (b) How much conservative work was done on this system? (c) How much non-conservative work was done on this organisation? (d) Verify the iii piece of work relations given in Equations eight-10.
Solution:

Affiliate 8 Potential Energy And Conservation Of Free energy Q.52P
A xv,800-kg truck is moving at 12.0 m/s when it starts down a 6.00° incline in the Canadian Rockies. At the start of the descent the commuter notices that the distance is 1630 thou. When she reaches an distance of 1440 chiliad, her speed is 29.0 m/southward. Find the change in (a) the gravitational potential free energy of the system and (b) the truck's kinetic free energy. (c) Is the total mechanical energy of the system conserved? Explain.
Solution:

Affiliate viii Potential Energy And Conservation Of Energy Q.53P
A 1.80-kg block slides on a rough horizontal surface. The block hits a leap with a speed of two.00 m/s and compresses it a altitude of xi.0 cm before coming to rest. If the coefficient of kinetic friction between the cake and the surface is µk = 0.560, what is the force constant of the spring?
Solution:

Chapter viii Potential Energy And Conservation Of Energy Q.54P

Solution:


The above effigy shows that, the object is at rest at initial point A. As the object moves from A to B, some of its potential energy is converted into kinetic free energy, and the speed of the object increases at B. So the kinetic free energy of the object increases when potential free energy decreases.
Now the object moves from indicate B to point C. In this procedure, some of its kinetic free energy is again converted into potential energy, thus, the speed of the object decreases every bit it moves from B to C. The object's speed once again increases equally it moves from indicate C to bespeak D, so its potential energy decreases while its kinetic free energy increases.
Finally from point D to point E, the kinetic energy of the object decreases as bend rises. Thus, the speed of the object decreases. Therefore, at point E, the speed of the object momentarily becomes zero.

Affiliate viii Potential Energy And Conservation Of Energy Q.55P

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Chapter viii Potential Energy And Conservation Of Energy Q.56P

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Chapter eight Potential Energy And Conservation Of Energy Q.57P
A 23-kg child swings dorsum and along on a swing suspended by 2.5-m-long ropes. Plot the gravitational potential free energy of this organisation equally a function of the bending the ropes make with the vertical, assuming the potential energy is zero when the ropes are vertical. Consider angles upward to 90° on either side of the vertical.
Solution:

Chapter eight Potential Energy And Conservation Of Energy Q.58P
Find the turning-indicate angles in the previous problem if the child has a speed of 0.89 m/s when the ropes are vertical. Indicate the turning points on a plot of the system's potential energy.
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.59P

Solution:

Affiliate 8 Potential Energy And Conservation Of Free energy Q.60P
A block of mass k = 0.95 kg is connected to a leap of force abiding k = 775 N/m on a shine, horizontal surface. (a) Plot the potential free energy of the jump from x = −5.00 cm to 10 = 5.00 cm. (b) Determine the turning points of the block if its speed at x = 0 is 1.three chiliad/s.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.61P
A ball of mass 1000 = 0.75 kg is thrown straight upward with an initial speed of 8.9 m/s. (a) Plot the gravitational potential energy of the block from its launch meridian, y = 0, to the height y = v.0 m. Let u = 0 stand for to y = 0. (b) Make up one's mind the turning bespeak (maximum height) of this mass.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.62P
2 blocks, the of mass m, are continued on a frictionless horizontal table by a spring of force constant k and equilibrium length L. Find the maximum and minimum separation between the 2 blocks in terms of their maximum speed, vmax,relative to the table. (The two blocks ever motility in opposite directions as they oscillate back and forth well-nigh a fixed position.)
Solution:

Chapter 8 Potential Energy And Conservation Of Free energy Q.63GP
Yous and a friend both solve a trouble involving a skier going down a gradient. When comparing solutions, you detect that your selection for the y = 0 level is different than the y = 0 level chosen past your friend. Will your answers agree or disagree on the post-obit quantities: (a) the skier's potential free energy; (b) the skier'southward change in potential free energy; (c) the skier's kinetic energy?
Solution:
Respond:
Your answers volition disagree on (a), but concur on (b) and (c)
The gravitational potential energy depends upon the reference level merely not the modify in potential energy. The work done by gravity must exist the same in the ii solutions so change in potential energy and change in kinetic free energy should be same.

Chapter eight Potential Energy And Conservation Of Energy Q.64GP
A particle moves under the influence of a conservative force. At indicate A the particle has a kinetic energy of 12 J; at point xiii the particle is momentarily at rest, and the potential energy of the system is 25 J; at point C the potential energy of the system is five J. (a) What is the potential energy of the system when the particle is at betoken A? (b) What is the kinetic energy of the particle at betoken C?
Solution:
(a) In the given data the particle is at residue at point B having potential free energy 25J. Therefore the total free energy of the particle is 25J.
Now at point A the particle has kinetic energy of 12J.
Therefore the potential energy of the system at betoken A is 25J-12J=13J
(b) Now at bespeak C the particle has potential energy of 5J.
Therefore the kinetic free energy of the system at point C is 25J-5J=20J

Chapter eight Potential Energy And Conservation Of Energy Q.65GP
A leaf falls to the footing with constant speed. Is ui + Ki for this system greater than, less than, or the aforementioned as uf + Kf for this system? Explicate.
Solution:

Chapter 8 Potential Energy And Conservation Of Free energy Q.66GP
Consider the 2-cake organisation shown in Example. (a) Equally cake 2 descends through the distance d, does its mechanical energy increment, decrease, or stay the same? Explain. (b) Is the nonconservative work done on block ii by the tension in the rope positive, negative, or zero? Explain.
Solution:
Solution:
(a) Since there is no conservative work with this system (the friction from mass one) the mechanical energy of the system will change. Specifically, the mechanical free energy of the system volition decrease due to free energy being converted into heat by the friction forces.
(b) The tension in the rope deals with the weight of the block that'southward dropping down. The not conservative force comes from the friction of the block on the table. The tension in the rope just deals with mass and gravitational acceleration thus, the tension in the rope is involved in potential/kinetic free energy relations, and the amount of non conservative work it does is zippo.

Chapter viii Potential Free energy And Conservation Of Energy Q.67GP
Taking a bound of faith, a bungee jumper steps off a plat-course and falls until the string brings her to rest. Suppose you lot analyze this system past choosing y = 0 at the platform level, and your friend chooses y = 0 at ground level. (a) Is the jumper's initial potential energy in your calculation greater than, less than, or equal to the same quantity in your friend's calculation? Explicate. (b) Is the modify in the jumper's potential energy in your calculation greater than, less than, or equal to the aforementioned quantity in your friend'southward calculation? Explain.
Solution:

Chapter eight Potential Energy And Conservation Of Energy Q.68GP
A sled slides without friction downwardly a modest, ice-covered hill. If the sled starts from residue at the top of the hill, its speed at the lesser is 7.50 thou/due south. (a) On a 2d run, the sled starts with a speed of 1.50 m/s at the top. When information technology reaches the bottom of the hill, is its speed 9.00 m/s, more 9.00 k/s, or less than nine.00 one thousand/s? Explain. (b) Find the speed of the sled at the bottom of the loma after the second run.
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.69GP
In the previous problem, what is the height of the loma?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.70GP

Solution:

Affiliate viii Potential Energy And Conservation Of Energy Q.71GP
Running Shoes The soles of a popular make of running shoe have a force constant of 2.0 × 105 North/chiliad. Treat the soles as ideal springs for the following questions. (a) If a 62-kg person stands in a pair of these shoes, with her weight distributed equally on both feet, how much does she compress the soles? (b) How much free energy is stored in the soles of her shoes when she's standing?
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.72GP
Nasal Strips The strength required to flex a nasal strip and apply it to the nose is 0.25 North; the energy stored in the strip when flexed is 0.0022 J. Assume the strip to be an ideal spring for the following calculations. Notice (a) the altitude through which the strip is flexed and (b) the force constant of the strip.
Solution:

Affiliate eight Potential Energy And Conservation Of Free energy Q.73GP
A pendulum bob with a mass of 0.13 kg is attached to a cord with a length of 0.95 yard. Nosotros choose the potential free energy to be nada when the string makes an angle of 90° with the vertical. (a) Find the potential energy of this arrangement when the string makes an bending of 45° with the vertical. (b) Is the magnitude of the change in potential energy from an angle of 90° to 45° greater than, less than, or the same as the magnitude of the change from 45° to 0°? Explicate. (c) Calculate the potential energy of the system when the string is vertical.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.74GP

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.75GP
An 1865-kg airplane starts at rest on an airdrome runway at sea level. (a) What is the change in mechanical energy of the aeroplane if it climbs to a cruising altitude of 2420 m and maintains a constant speed of 96.v m/s? (b) What cruising speed would the plane demand at this altitude if its increment in kinetic energy is to be equal to its increase in potential energy?
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.76GP
At the local playground a child on a swing has a speed of 2.02 m/s when the swing is at its lowest-point. (a) To what maximum vertical pinnacle does the child rise, assuming he sits still and "coasts"? Ignore air resistance. (b) How do your results change if the initial speed of the child is halved?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.77GP

Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.78GP

Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.79GP
A person is to be released from rest on a swing pulled away from the vertical past an angle of xx.0°. The 2 frayed ropes of the swing are 2.75 m long, and will break if the tension in either of them exceeds 355 N. (a) What is the maximum weight the person can accept and non interruption the ropes? (b) If the person is released at an bending greater than xx.0°, does the maximum weight increase, decrease, or stay the same? Explain.
Solution:

Chapter eight Potential Energy And Conservation Of Free energy Q.80GP
A car is benumbed without friction toward a loma of height h and radius of curvature r. (a) What initial speed, v0, will upshot in the car's wheels simply losing contact with the roadway as the motorcar crests the colina? (b) What happens if the initial speed of the auto is greater than the value institute in part (a)?
Solution:

Chapter eight Potential Energy And Conservation Of Energy Q.81GP

Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.82GP

Solution:

Affiliate 8 Potential Free energy And Conservation Of Energy Q.83GP
An 8.70-kg block slides with an initial speed of one.56 one thousand/s up a ramp inclined at an angle of 28.4° with the horizontal. The coefficient of kinetic friction betwixt the cake and the ramp is 0.62. Use energy conservation to find the distance the cake slides earlier coming to residue.
Solution:

Affiliate 8 Potential Energy And Conservation Of Energy Q.84GP
Echo the previous trouble for the case of an 8.70-kg block sliding downwardly the ramp, with an initial speed of 1.56 one thousand/s.
Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.85GP
Jeff of the Jungle swings on a 7.6-g vine that initially makes an angle of 37° with the vertical. If Jeff starts at restand has a mass of 78 kg, what is the tension in the vine at the everyman point of the swing?
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.86GP

Solution:

Affiliate eight Potential Energy And Conservation Of Energy Q.87GP

Solution:

Chapter 8 Potential Energy And Conservation Of Free energy Q.88GP
Compressing the Ground A running rails at Harvard University uses a surface with a force constant of ii.v × 105 N/m This surface is compressed slightly every time a runner's foot lands on it. The strength exerted by the foot, according to the Saucony shoe company, has a magnitude of 2700 North for a typical runner. Treating the track'south surface as an platonic spring, observe (a) the amount of compression caused past a human foot hitting the rails and (b) the energy stored briefly in the runway every time a foot lands.
Solution:

Chapter 8 Potential Energy And Conservation Of Free energy Q.89GP
A Flea's Bound The resilin in the upper leg (coxa) of a flea has a force constant of about 26 Northward/m, and when the Flea cocks its jumping legs, the resilin in the leg is stretched by approximately 0.10 mm. Given that the flea has a mass of 0.fifty mg, and that two legs are used in a jump, guess the maximum height a flea can attain by using the energy stored in the resilin. (Assume the resilin to be an ideal spring.)
Solution:

Affiliate viii Potential Energy And Conservation Of Energy Q.90GP
A trapeze creative person of mass yard swings on a rope of length L. Initially, the trapeze artist is at residual and the rope makes an bending θ with the vertical. (a) Observe the tension in the rope when information technology is vertical. (b) Explain why your result for part (a) depends on L in the way information technology does.
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.91GP

Solution:

Chapter eight Potential Energy And Conservation Of Energy Q.92GP

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.93GP

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.94GP

Solution:

Affiliate viii Potential Energy And Conservation Of Energy Q.95GP

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.96GP

Solution:

Chapter viii Potential Energy And Conservation Of Free energy Q.97GP

Solution:

Chapter viii Potential Energy And Conservation Of Free energy Q.98GP

Solution:

Affiliate eight Potential Energy And Conservation Of Energy Q.99GP

Solution:

Chapter viii Potential Free energy And Conservation Of Free energy Q.100PP
The Flying of the Dragonflies
Of all the animals yous're probable to encounter on a summertime'south day, the most ancient is the dragonfly. In fact, the fossil record for dragonflies extends dorsum over 250 million years, more twice as long equally for birds. Ancient dragonflies could be as large as a militarist, and were surely buzzing around the heads of both T. King and Triceratops.
Dragonflies vest to the order Odonata ("toothed jaws") and the suborder Anisoptera ("different wings"), a reference to the fact that their hindwings are wider front-to-back than their forewings. (Damselflies, in contrast, have forewings and hind-wings that are the same.) Although aboriginal in their lineage, dragonflies are the fastest flying and most acrobatic of all insects; some of their maneuvers subject field them to accelerations equally corking as 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, have been of great interest to biologists. Figure shows an experimental setup designed to measure the strength constant of Plexiglas models of wings, which are used in wind tunnel tests. A downward forcefulness is practical to the model wing at the tip (1 for hindwing, two for forewing) or at two-thirds the distance to the tip (three for hindwing, iv for forewing). As the forcefulness is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Effigy. Detect that significant differences are seen between the hindwings and forewings, as one might expect from their different shapes.

Solution:

Affiliate viii Potential Energy And Conservation Of Energy Q.101PP
The Flight of the Dragonflies
Of all the animals you're likely to see on a summer's 24-hour interval, the most ancient is the dragonfly. In fact, the fossil record for dragonflies extends back over 250 million years, more than twice as long equally for birds. Ancient dragonflies could be as large equally a hawk, and were surely buzzing around the heads of both T. Rex and Triceratops.
Dragonflies belong to the gild Odonata ("toothed jaws") and the suborder Anisoptera ("different wings"), a reference to the fact that their hindwings are wider front-to-back than their forewings. (Damselflies, in contrast, have forewings and hind-wings that are the same.) Although aboriginal in their lineage, dragonflies are the fastest flying and nearly acrobatic of all insects; some of their maneuvers subject them to accelerations equally smashing every bit 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, accept been of not bad involvement to biologists. Figure shows an experimental setup designed to measure the force constant of Plexiglas models of wings, which are used in air current tunnel tests. A downward force is applied to the model wing at the tip (1 for hindwing, 2 for forewing) or at 2-thirds the distance to the tip (iii for hindwing, 4 for forewing). As the force is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Figure. Notice that pregnant differences are seen between the hindwings and forewings, as i might expect from their different shapes.

Solution:

Chapter 8 Potential Free energy And Conservation Of Energy Q.102PP
The Flight of the Dragonflies
Of all the animals yous're likely to run into on a summertime'due south twenty-four hour period, the most aboriginal is the dragonfly. In fact, the fossil record for dragonflies extends back over 250 million years, more than twice every bit long every bit for birds. Aboriginal dragonflies could be every bit big equally a hawk, and were surely buzzing around the heads of both T. Male monarch and Triceratops.
Dragonflies belong to the order Odonata ("toothed jaws") and the suborder Anisoptera ("different wings"), a reference to the fact that their hindwings are wider forepart-to-back than their forewings. (Damselflies, in contrast, accept forewings and hind-wings that are the same.) Although ancient in their lineage, dragonflies are the fastest flying and most acrobatic of all insects; some of their maneuvers subject them to accelerations as great every bit 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, have been of great interest to biologists. Figure shows an experimental setup designed to measure the force constant of Plexiglas models of wings, which are used in wind tunnel tests. A downwardly force is applied to the model fly at the tip (i for hindwing, two for forewing) or at two-thirds the altitude to the tip (3 for hindwing, 4 for forewing). Every bit the forcefulness is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Figure. Observe that significant differences are seen between the hindwings and forewings, as one might look from their different shapes.

Solution:
From the graph it is articulate that past the application of aforementioned force the deflection of wing is more for hindwing than the forewing.
Therefore force constant of forewing is greater than the forcefulness constant of hindwing.
So forewing is stiffer than the hindwing.
Therefore option B. is correct.

Affiliate 8 Potential Energy And Conservation Of Energy Q.103PP

Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.104IP
Referring to Example Consider a jump with a force abiding of 955 Due north/m. (a) Suppose the mass of the block is 1.70 kg, but its initial speed can exist varied. What initial speed is required to give a maximum spring compression of 4.00 cm? (b) Suppose the initial speed of the block is 1.09 m/s, but its mass can be varied. What mass is required to give a maximum bound compression of four.00 cm?
Solution:

Chapter 8 Potential Energy And Conservation Of Free energy Q.105IP
Referring to Case Suppose the cake is released from rest with the bound compressed 5.00 cm. The mass of the block is one.70 kg and the force abiding of the spring is 955 N/m. (a) What is the speed of the block when the jump expands to a pinch of only 2.l cm? (b) What is the speed of the block after information technology leaves the jump?
Solution:

Chapter 8 Potential Free energy And Conservation Of Free energy Q.106IP
Referring to Example Suppose we would like the landing speed of block 2 to be increased to 1.fifty m/due south. (a) Should the coefficient of kinetic friction betwixt block i and the table-acme exist increased or decreased? (b) Notice the required coefficient of kinetic friction for a landing speed of 1.50 m/s. Notation that m1 = ii.40 kg, m2 = 1.80 kg, and d = 0.500 m.
Solution:

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